arXiv subjects

L. Andrianopoli

Publications and source records attributed to L. Andrianopoli.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Implementation of the Constraints in Conformal Gravity

We propose a first-order geometric Lagrangian for four-dimensional conformal gravity within the Cartan formulation, which yields, dynamically, the standard constraints on the fields, expected for conformal gravity. Upon imposing the dynamical constraints, together with the request of conformal invariance of the off-shell Lagrangian, the theory reduces to the standard expression for conformal gravity, in terms of quadratic curvature invariants. Our results clarify the geometric status of conformal gravity as a gauge theory and open the way to a similar dynamical implementation of the constraints in higher dimensions and supersymmetric extensions.

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arXiv2022

M5-brane in the superspace approach

Motivated by Sen's spacetime prescription for the construction of theories with self-dual field strengths, we present a rigid superspace Lagrangian describing noninteracting tensor multiplets living on a stack of M5-branes and containing all the physical constraints on the fields, yielding the on-shell matching of the degrees of freedom. The geometric superspace approach adopted here offers a natural realization of superdiffeomorphisms and is particularly well suited for the coupling to supergravity. However, within this formulation the (anti-)self-duality property of the 3-form field strengths is lost when the superspace Lagrangian is trivially restricted to spacetime. We propose two main paths to address this issue: a first-order superspace extension of Sen's spacetime results, which, once trivially restricted to spacetime, yields all the dynamical equations including the (anti-)self-duality constraint on the 3-form field strengths, and a possible way to obtain a full superspace description of the theory, based on integral forms.

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arXiv2021

Twisting D(2,1; α) Superspace

We develop a three-dimensional $\mathcal{N}=4$ theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets $(Λ^{αα'\dotα'}_I,\,ϕ^{αA}_I)$ on a curved AdS$_3$ worldvolume background, whose supersymmetry is captured by the supergroup ${\rm D}^2(2,1;\, \boldsymbolα)$. To unveil some remarkable features of this model, we perform two twists, involving the SL$(2,\mathbb R)$ factors of the theory. After the first twist, our spacetime Lagrangian exhibits a Chern-Simons term associated with an odd one-form field, together with a fermionic "gauge-fixing'', in the spirit of the Rozansky-Witten model. The second twist allows to interpret the ${\rm D}^2(2,1;\, \boldsymbolα)$ setup as a framework capable of describing massive Dirac particles. In particular, this yields a generalisation of the Alvarez-Valenzuela-Zanelli model of ''unconventional supersymmetry''. We comment on specific values of the combination $α+1$, which in our model is related to a sort of gauging in the absence of dynamical gauge fields.

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arXiv2021

$\mathcal N=2$ AdS$_4$ supergravity, holography and Ward identities

We develop in detail the holographic framework for an $\mathcal{N}=2$ pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding superconformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super-AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.

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arXiv2020

$\mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene

We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, ${\bf K}$ and ${\bf K}'$. The two valleys correspond to the two independent sectors of the ${\rm OSp}(p|2)\times {\rm OSp}(q|2)$ boundary model in the $p=q$ case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model.

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arXiv2019

The Quantum Theory of Chern-Simons Supergravity

We consider $AdS_3$ $N$-extended Chern-Simons supergravity (à la Achucarro-Tonswend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion.

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arXiv2018

Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity

In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2) invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, for specific spatial geometries. Our construction yields the model in [Alvarez:2011gd] with a specific prescription on the parameters. In this framework the Dirac spin-1/2 fermion originates from the radial components of the gravitini in D=4.

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arXiv2017

More on the Hidden Symmetries of 11D Supergravity

In this paper we clarify the relations occurring among the osp(1|32) algebra, the M-algebra and the hidden superalgebra underlying the Free Differential Algebra of D=11 supergravity (to which we will refer as DF-algebra) that was introduced in the literature by D'Auria and Fré in 1981 and is actually a (Lorentz valued) central extension of the M-algebra including a nilpotent spinor generator, Q'. We focus in particular on the 4-form cohomology in 11D superspace of the supergravity theory, strictly related to the presence in the theory of a 3-form $A^{(3)}$. Once formulated in terms of its hidden superalgebra of 1-forms, we find that $A^{(3)}$ can be decomposed into the sum of two parts having different group-theoretical meaning: One of them allows to reproduce the FDA of the 11D Supergravity due to non-trivial contributions to the 4-form cohomology in superspace, while the second one does not contribute to the 4-form cohomology, being a closed 3-form in the vacuum, defining however a one parameter family of trilinear forms invariant under a symmetry algebra related to osp(1|32) by redefining the spin connection and adding a new Maurer-Cartan equation. We further discuss about the crucial role played by the 1-form spinor $η$ (dual to the nilpotent generator Q') for the 4-form cohomology of the eleven dimensional theory on superspace.

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arXiv2016

Hidden Gauge Structure of Supersymmetric Free Differential Algebras

The aim of this paper is to clarify the role of the nilpotent fermionic generator Q' introduced in Ref. [3] and appearing in the hidden supergroup underlying the free differential algebra (FDA) of D=11 supergravity. We give a physical explanation of its role by looking at the gauge properties of the theory. We find that its presence is necessary, in order that the extra 1-forms of the hidden supergroup give rise to the correct gauge transformations of the p-forms of the FDA. This interpretation is actually valid for any supergravity containing antisymmetric tensor fields, and any supersymmetric FDA can always be traded for a hidden Lie superalgebra containing extra fermionic nilpotent generators. As an interesting example we construct the hidden superalgebra associated with the FDA of N=2, D=7 supergravity. In this case we are able to parametrize the mutually non local 2- and 3-form B^(2) and B^(3) in terms of hidden 1-forms and find that supersymmetry and gauge invariance require in general the presence of two nilpotent fermionic generators in the hidden algebra. We propose that our approach, where all the invariances of the FDA are expressed as Lie derivatives of the $p$-forms in the hidden supergroup manifold, could be an appropriate framework to discuss theories defined in enlarged versions of superspace recently considered in the literature, such us double field theory and its generalizations.

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arXiv2013

Entropy Current Formalism for Supersymmetric Theories

The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to supersymmetric theories and supergravities. We formulate a new entropy current in superspace with the properties: 1) it is conserved off-shell for non dissipative fluids, 2) it is invariant under rigid supersymmetry transformations 3) it is covariantly closed in local supersymmetric theories 4) it reduces to its bosonic expression on space-time.

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arXiv2013

A Note on the Field-Theoretical Description of Superfluids

Recently, a Lagrangian description of superfluids attracted some interest from the fluid/gravity-correspondence viewpoint. In this respect, the work of Dubovksy et al. has proposed a new field theoretical description of fluids, which has several interesting aspects. On another side, we have provided in arXiv:1304.2206 a supersymmetric extension of the original works. In the analysis of the Lagrangian structures a new invariant appeared which, although related to known invariants, provides, in our opinion, a better parametrisation of the fluid dynamics in order to describe the fluid/superfluid phases.

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arXiv2011

Two-Centered Magical Charge Orbits

We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product (Q1,Q2), known to control the mutual non-locality of the two centers.

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arXiv2010

Fake Superpotential for Large and Small Extremal Black Holes

We consider the fist order, gradient-flow, description of the scalar fields coupled to spherically symmetric, asymptotically flat black holes in extended supergravities. Using the identification of the fake superpotential with Hamilton's characteristic function we clarify some of its general properties, showing in particular (besides reviewing the issue of its duality invariance) that W has the properties of a Liapunov's function, which implies that its extrema (associated with the horizon of extremal black holes) are asymptotically stable equilibrium points of the corresponding first order dynamical system (in the sense of Liapunov). Moreover, we show that the fake superpotential W has, along the entire radial flow, the same flat directions which exist at the attractor point. This allows to study properties of the ADM mass also for small black holes where in fact W has no critical points at finite distance in moduli space. In particular the W function for small non-BPS black holes can always be computed analytically, unlike for the large black-hole case.

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arXiv2009

First Order Description of D=4 static Black Holes and the Hamilton-Jacobi equation

In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow coincides with the Hamilton principal function associated with the one-dimensional effective Lagrangian. This implies that the prepotential can always be defined, at least locally in the radial variable and in the moduli space, both in the extremal and non-extremal case and allows us to conclude that it is duality invariant. We also give, in this framework, a general definition of the ``Weinhold metric'' in terms of which a necessary condition for the existence of multiple attractors is given. The Hamilton-Jacobi formalism can be applied both to the restricted phase space where the electromagnetic potentials have been integrated out as well as in the case where the electromagnetic potentials are dualized to scalar fields using the so-called three-dimensional Euclidean approach. We give some examples of application of the formalism, both for the BPS and the non-BPS black holes.

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arXiv2008

Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules

We study the gauging of the orthosymplectic algebras OSp(6|4)xSO(2) and its "dual" OSp(2|4)x SO(6), both based on supergravities with the same exceptional coset SO*(12)/U(6), and gauge group SO(6)xSO(2). The two dual theories are obtained by two different truncations of gauged N=8 AdS_4 supergravity. We explicitly study the gauge sector of the two dual theories with the most general group allowed by supersymmetry. In the ungauged (super-Poincaré) case they exhibit the same (large) black-hole attractor solutions with dual relations between the 1/N-BPS and non-BPS configurations. The N=6 gravity multiplet has also the exceptional property to be a {\em zero-center module} of OSp(6|4), as it is the case for superconformal Yang--Mills theory in four dimensions based on SU(2,2|n) (PSU(2,2|4) for n=4) or OSp(n|4).

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arXiv2007

Non-BPS Attractors in 5d and 6d Extended Supergravity

We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.

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arXiv2005

Gauge Charges from Supergravity

Some recent results in the study of four dimensional supergravity flux compactifications are reviewed, discussing in particular the role of torsion on the compactification manifold in generating gauge charges for the effective four dimensional theories.

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arXiv2005

The Scherk-Schwarz mechanism as a flux compactification with internal torsion

The aim of this paper is to make progress in the understanding of the Scherk-Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E6(6) S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can be directly identified with certain components of the four-form field-strength. Furthermore, we introduce a novel (four dimensional) approach to the study of dualities between flux/torsion compactifications of Type II/M-theory. This approach defines the action that duality should have on the background quantities, in order for the E7(7) invariance of the field equations and Bianchi identities to be restored also in the presence of fluxes/torsion. This analysis further implies the interpretation of the torsion flux as the T-dual of the NS three-form flux.

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